Hi there -- when I said "the first one" I meant the first one posed by KarlS -- in the case of my three, the first one is easy -- as you say the answer is independent of the size of the planet (my specifying the diameter was a "red-herring") -- but you'd be amazed how many folks have difficulty with this one until you explain it (which I don;t want to do here so as to not give the game away)
Re: Puzzle 2. As an engineering approximation, assume that the tank has a hexagonal cross-section. Hence, mark
1/6 full 1/4 way up the stick, 1/3 at 3/8, 1/2 at 1/2, 2/3 at 3/8, and 5/6 full at 3/4. That should do for a start.
Otherwise, invert the formula for a circlar sector.
I like KarlS's first puzzle. Solve t - 1 = t!
If one car starts out at 30 mph and a second starts out an hour later at 60 mph, how long before the second car has gone twice as far as the first? (ignore acceleration time).
At what times are the hands on a clock pointing in exactly opposite directions?
Assuming a balance beam scale (with counterweights) for puzzle #3 makes the math very easy. Exactly 100 Kg. A strain gauge scale takes some brain sweat with centripetal force calculations. 99.67 Kg ?
#2 14.9 cm and 35.1 cm ? Circle segment area geometry, not calculus. Chords and arcs and all that neat stuff long since forgotten. Thank goodness for Wikipedia. Now my head hurts...
These are interesting puzzles. Looking forward to more.
Hi Max. Ref problem no. 1. The answer is easy, I won't give it away though, but the main problem that occurs to me is, how are you going to drive the wooden sticks into your stainless steel planet?
I think No. 2 requires calculus, which I tried to relearn recently, this would be a good test of my knowledge...